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The study on neural systems is very hot, especially regarding modelling of fuzzy neural networks. The neuron models have been limited in interval [0,1] before. This paper studies the logic operators and neuron models of proposition object based on [a, b]. Any interval [a, b] is called a generalized interval. Firstly, authors provide the conception of proposition object, discussed on the radix space of universal logic. Secondly, using the NTS norms theories, this paper establishes the universal logic operation models on generalized interval [a, b]. Thirdly, the paper builds up a new uniform neuron model of "Not/And/Or/Average" on generalized interval [a, b]. As an instance, authors discuss the neuron models based on standard interval [0,1], which are continuously changeable with generalized correlation coefficient "h" and generalized self-correlation coefficient "k". This work offers important theories and models for neurons reasoning, make it more flexible because of the change of h, k and [a, b], and enlarge its study domain. [ABSTRACT FROM AUTHOR]